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Hypothesis Testing of Mean & Proportion

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Please assist with answering the following questions attached dealing with Hypothesis Testing.

Hypothesis Testing

Setting Up Hypothesis

1. For the following problem statement, identify the null hypothesis H0 and the alternative hypothesis H1. Suppose that a mayor claims that the mean salary for the working professionals in the downtown metropolitan area of Los Diablos is \$42,000. A sample of 35 randomly selected working professionals in the area yields a mean of \$39,367 with a sample standard deviation of \$ 7,548. At the a=0.05 significance level, test his claim.

Null Hypothesis =

Alternative Hypothesis =

2. For the following problem statement, identify the null hypothesis H0 and the alternative hypothesis H1. Suppose that Overtime.com claims that their weekly losses are no more than \$2500. A sample of 40 random weeks finds a mean weekly loss of \$3200 with an estimate population standard deviation of \$750. Test their claim at the a = 0.05 level

Null Hypothesis =

Alternative Hypothesis =

Tests about a Population Mean

1. Suppose that a company claims that their mean weekly sales are \$12,250. A random sample of 35 weeks yields a sample mean of x = \$9575, with a sample standard deviation of s= \$1250. Given that the pair of hypothesis that correspond to the claim are:

H0: &#956; = 12,250
H1: &#956; (not = to) 12,250

Find the critical values for the hypothesis test. Assume that the significance level is a= 0.05.

Z = (plus over minus symbol)

Round your final answer to two decimal places.

2.Suppose that a small college claims that they graduate at least 500 students every semester. A random sample of 31 semesters yields a sample mean of x = 420, with a sample standard deviation of s = 65. Given that the pair of hypothesis that correspond to the claim are:

H0: &#956; greater or = to 500
H1: &#956; less than 500

Find the critical values for the hypothesis test. Assume that the significance level is a= 0.02.

Z =

Round your final answer to two decimal places.

3. Suppose that an insurance agent claims that the average life insurance policy premium that he sells is \$500 per year. A sample of 45 customers yields a mean of x = \$575 and a standard deviation of s = \$65. You decide to test his claim at the a= 0.02 significance level. If the hypothesis are:

H0: &#956; = to 500

H1: &#956; not = to 500

With critical values of + 2.33, compute the sample statistic, and choose the appropriate conclusion.
_
Z =

Round your final answer to two decimal places.

Based on the sample statistic, we:

a.cannot reject Ho, this the average premium is not \$500
b.reject Ho, thus the average premium is not \$500
c. cannot reject Ho, thus the average premium may be \$500
d. reject Ho, thus the average premium may be different from \$500

4. Suppose that a company CEO claims that the average severance package for an employee at his company is \$500,000. You decided to test his claim using a significance level of a=0.05. A sample of 55 employees yield a mean of x=\$485,155 with a sample standard deviation of s = \$ 125,575. First, you set up your hypothesis as follows:

H0: &#956; = to \$500,000 (claim)

H1: &#956; not = to \$500,000

Then you compute your sample statistic, and get the following:

Z = 485,155 - 500,000
125,575
55
= - .8767

Compute the probability of getting a sample statistic at least as extreme as z= -0.8767, and interpret this probability value.

Probability =

Round your final answer to two decimal places.

Based on a comparison of a = 0.05 significance level with your p-value:

a. there is enough evidence to reject the claim
b. there is not enough evidence to reject the claim
c. there is evidence that proves the claim
d. there is no evidence that supports the claim

Tests about a population proportion
1.Suppose that a company claims that 67% of their employees (about 2/3 ) buy annual parking permits for parking at their workplace. A random survey of 120 employees finds that 62 of them have annual parking permits. Given that the pair of hypothesis that correspond to the claim are as follows:

H0: p = 0.67

H1: p not = to 0.67

Find the critical values for the hypothesis test. Assume that the significance level is a= 0.01

Z = +
-
Round your final answer to two decimal places.

2. Suppose that a small college claims a majority of their students graduate within four years. A random survey of 250 alumni finds that 145 of them graduated within 4 years. Given that the pair of hypothesis that correspond to the claims are as follows:

H0: p is < or = 0.50

H1: p is > 0.50

Find the critical value for the hypothesis test. Assume that the significance level is a = 0.03.

Z =

Round your final answer to two decimal places.

3. Suppose that an insurance agent claims that less that 5% of his life insurance policies ever have to "pay out". You decide to test his claim at the a = 0.01 significance level. A sample of 100 policies from last year finds that 7 of them had to pay out. If the hypothesis are:

H0: p is > or = 0.50
H1: p is < 0.50

With a critical value of -2.33, compute the sample statistic, and choose the appropriate conclusion.

Z =

Round your final answer to two decimal places.

Based on the sample statistic:

a.we cannot reject Ho, thus at least 5% of the policies pay out
b.we reject Ho, thus less that 5% of the policies pay out
c. we cannot reject Ho, thus it may be that at least 5% of the policies pay out
d. we reject Ho, thus it may be that 5% of the policies pay out

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Solution Preview

Please see the attachments.

Hypothesis Testing

Setting up Hypothesis
1. For the following problem statement, identify the null hypothesis H0 and the alternative hypothesis H1. Suppose that a mayor claims that the mean salary for the working professionals in the downtown metropolitan area of Los Diablos is \$42,000. A sample of 35 randomly selected working professionals in the area yields a mean of \$39,367 with a sample standard deviation of \$ 7,548. At a=0.05 significance level, test his claim.
Null Hypothesis:
H0: Mean salary for the working professionals in the downtown metropolitan area of Los Diablos = \$42,000 (µ = 42,000)
Alternative Hypothesis:
H1: Mean salary for the working professionals in the downtown metropolitan area of Los Diablos ≠ \$42,000 (µ ≠ 42,000)
The test statistic used is . Given that = 39,367, n = 35,  = 7548
Therefore, = -2.063730534
Rejection Criteria: Reject the null hypothesis, if the absolute value of calculated Z is greater than the critical value of Z at the 0.05 significance level.
Critical value = ±1.959963985
Conclusion: Reject the null hypothesis, since the absolute value of calculated Z is greater than the critical value. The sample does not provide enough evidence to support the claim that the mean salary for the working professionals in the downtown metropolitan area of Los Diablos is \$42,000.
Details
Z Test of Hypothesis for the Mean

Data
Null Hypothesis = 42000
Level of Significance 0.05
Population Standard Deviation 7548
Sample Size 35
Sample Mean 39367

Intermediate Calculations
Standard Error of the Mean 1275.844863
Z Test Statistic -2.063730534

Two-Tail Test
Lower Critical Value -1.959963985
Upper Critical Value 1.959963985
p-Value 0.039043273
Reject the null hypothesis

2. For the following problem statement, identify the null hypothesis H0 and the alternative hypothesis H1. Suppose that Overtime.com claims that their weekly losses are no more than \$2500. A sample of 40 random weeks finds a mean weekly loss of \$3200 with an estimate population standard deviation of \$750. Test their claim at the a = 0.05 level
Null Hypothesis:
H0: Mean weekly losses of Overtime.com ≤ \$2500 (µ ≤ 2500)
Alternative Hypothesis:
H1: Mean weekly losses of Overtime.com > \$2500 (µ > 2500)
The test statistic used is . Given that = 3200, n = 40,  = 750
Therefore, = 5.902918299
Rejection Criteria: Reject the null hypothesis, if the calculated value of Z is greater than the critical value of Z at the 0.05 significance level.
Critical value = 1.644853627
Conclusion: Reject the null hypothesis, since the calculated value of Z is greater than the critical value. The sample does not provide enough evidence to support the claim that the weekly losses of Overtime.com are no more than \$2500.
Details

Z Test of Hypothesis for the Mean

Data
Null Hypothesis = 2500
Level of Significance 0.05
Population Standard Deviation 750
Sample Size 40
Sample Mean 3200

Intermediate Calculations
Standard Error of the Mean 118.5854123
Z Test Statistic 5.902918299

Upper-Tail Test ...

Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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